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BOND MATH: The Theory Behind the Formulas by Donald J. Smith

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Chapter 6: Duration and Convexity

Equation 6.1 is the general bond pricing relationship between coupon payment dates. MV is the total price including accrued interest; PMT is the periodic coupon payment; FV is the principal redeemed in N periods as of the beginning of the current period, and t/T of the period has gone by and 1 – t/T remains.

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Multiply the numerator and denominator on the right side by (1 + y)t/T.

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Define the term in brackets to be PV, the price of the bond if the yield y prevailed at the beginning of the period when there were

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